Case Study 1: Audience Size

Executive Summary

The intent of this executive summary is to answer two questions.

Who listens to Sirius Radio?
Who listens to Sirius Business Radio by Wharton?
Does this sample appear to be a random sample from the general population?
Does this sample appear to be a random sample from the MTURK population?

Based on the responses of these answers we move forward with the following implications.

What method should be utilized to estimate the audience size?
what data should be collected and where should it come from?

The variables that were selected for analysis were, age, education, gender, income, sirius, wharton, and worktime. Survey questions that did not have a response were recoded to NA. Survey questions that were input in the incorrect format, were changed to be in the appropriate format. For example, age should have been a numeric input; however, some respondents wrote out their age that being ‘eighteen’ rather than 18. Other examples of incorrect information includes typing 223. The age 223, is far beyond the life span of a normal human. It cannot be assumed that the individual intended to type 22, 23, or 32. As such, this response was changed to NA.

Summary Tables

Who listens to Sirius Radio?
Who listens to Sirius Business Radio by Wharton?
Does this samples appear to be a random sample from the general population?
Does this sample appear to be a random sample from the MTURK population?

The first four questions can be responded to by analyzing the following figures.

Educational attainment

The summary table is split by educational attainment and shows that most listeners has some college or no diploma or has a bachelor’s degree. For the individuals who own a bachelor’s degree, the average age of the listener is 28.5 while the median is 26. For individuals who hold a bachelors degree, the mean age is 31.14 while the median is 28.

Education	Frequency	Mean_Age	Median_Age	Mean_Worktime	Median_Worktime
Less than 12 years; no high school diploma	10	30.00000	27.0	23.90000	22.0
High school graduate (or equivalent)	191	30.21466	27.0	23.32984	21.0
Some college, no diploma; or Associates degree	737	28.51967	26.0	22.49389	21.0
Bachelors degree or other 4-year degree	612	31.14379	28.0	21.96078	20.0
Graduate or professional degree	177	34.57627	31.0	23.22034	21.0
Other	2	50.50000	50.5	46.50000	46.5

Age

For a closer look at the age of listeners a frequency table has been included to show the gender breakdown with the mean and median age of male and female listeners.

Gender	Frequency	Mean_Age	Median_Age	Mean_Worktime	Median_Worktime
Female	729	31.9561	29	23.52812	21
Male	1000	29.0750	27	21.76400	20

Histogram of age which is split by gender and income also show the breakdown of age.

Income

A table has also been included below which shows the income level of participants of the survey. From the survey most participants had an income between $30,000 and $50,000. The mean age was 30 while the median was 28.

Income	Frequency	Mean_Age	Median_Age	Mean_Worktime	Median_Worktime
Less than $15,000	206	26.57767	24	21.19903	20.0
$15,000 - $30,000	360	29.45833	27	23.09167	21.0
$30,000 - $50,000	421	30.73634	28	22.85036	20.0
$50,000 - $75,000	372	31.46774	29	22.15860	20.0
$75,000 - $150,000	326	31.59202	30	22.80368	21.0
Above $150,000	44	30.59091	24	21.34091	20.5

Wharton and Sirius?

Box Plots

The box plot, below faceted by educational attainment and income specifically describes the users who listen to both Wharton radio and Sirius radio. Each of the boxplots are split by gender and describe the age of each listener.

Conclusion: Who listens to Wharton Radio?

Based on the charts above, the age of the average listeners tends to be mid 20’s to early 30’s. Usually they will have some educational background of some sort and more often tend to be male than female. Generally these individuals will be making $30,000 - $50,000 a year. Knowing the general audience base, the next two questions can be responded to.

What method should be utilized to estimate the audience size?
what data should be collected and where should it come from?

Method for estimating Audience Size?

This dataset generally represents a broad population. Based on this data we can infer the estimated audience size by filtering people who listen to sirius XM and people who listen to wharton’s podcast. This however, gives that aggregate audience size rather than individual downloads per podcast.

What data should be collected and where should it come from?

Rather than administering data from MTURK, a more direct approach to listener base can be found by pulling data from stitcher which has been aquired by Sirius XM. This data may provide more specific and provide helpful information such as age to rating. Further the data should describe gender identity and sex as a spectrum to be inclusive of individuals who do not identify as male or female as this can provide future topics that wharton professors can address.

Case Study 2: Women in Science

Questions

How many fields?
type of degrees?
years of statistics being reported

In this data set there are 10 different fields of study, 3 different degree levels and 11 years worth of data from 2006 - 2016. This can be seen in the summary tables below.

By Field and Sex

This table shows that 10 different fields of study and the total amount of Male and Female people who studied the field. Overall looking at the 10 fields, there is an even breakdown of Female dominated fields to Male dominated fields.

Field	Male	Female	More
Agricultural sciences	152956	172852	Female
Biological sciences	516556	745384	Female
Computer sciences	626248	171808	Male
Earth, atmospheric, and ocean sciences	53118	36076	Male
Engineering	1147112	301426	Male
Mathematics and statistics	173641	125083	Male
Non-S&E	7356720	11916324	Female
Physical sciences	194365	120797	Male
Psychology	326865	1109902	Female
Social sciences	1041377	1244592	Female

By Degree and Sex

This table shows the 3 different types of degrees over the course of 11 years with sex being broken down. The data shows that although there are more female people collectively receiving Bachelors degrees and Masters degrees, Male people attain more Ph.Ds.

Degree	Male	Female	More
BS	8137972	10930199	Female
MS	3104414	4669113	Female
PhD	346572	344932	Male

By Year and Sex

Finally the last table shows the amount of degrees attained each year by male and females. Showing that overall, female people overall earn more degrees and that there has been a stead increase of degrees over time.

Year	Male	Female	More
2006	904679	1253917	Female
2007	925621	1287439	Female
2008	953360	1320480	Female
2009	985411	1360820	Female
2010	1019514	1404646	Female
2011	1063992	1466539	Female
2012	1107721	1525402	Female
2013	1130821	1552075	Female
2014	1147769	1570559	Female
2015	1163164	1586060	Female
2016	1186906	1616307	Female

BS degrees in 2015

The summary statistics tables above are high level summaries. To understand the breakdown of science related fields vs non-science fields in 2015, separate bar plots have been made.

2015 Overall Science and Engineering This bar plot shows the breakdown of science and engineering fields and compares them to the broader category of non-science and engineering fields.

To show the difference in sex between Non-science and engineering fields and science and engineering fields in 2015 the following bar plot has been made. As the tables above show generally there are more woman obtaining degrees, which is highlighted by the larger Non-S&E bar. However; despite when comparing S&E, the bar for Male and Female, are almost similar in frequency.

Questions

In general, the summary tables show that there female people are overall earning more degrees; however, when broken down by science-related fields Female people generally study, social sciences, psychology, biology, and agricultural sciences. Male people study physical sciences, mathematics and statistics, engineering, earth, atmospheric, and ocean sciences, and computer Science. This can be found in the box plot below. This is consistent with literature that shows that these fields are often not inclusive of woman, and in particular women of color.

To see if woman are in the field of data science, the plot has been filtered to only include, computer science, math and statistics. Despite the foundations that woman have established in the fields of mathematics, statistics and computer science, woman are underrepresented in both fields.

Conclusion

Based on this dataset, there is a consistently lower proportion of women in science-related fields across years. However, it remains unclear which fields consisted of the non-SE related fields, or why the above nine fields were chosen to represent “Science-related” fields. Other fields, such as chemical sciences and medical and health sciences, among others, belong to science as well. Future studies could improve by asking participants to clarify their degree fields in the data collection process.

Case Study 3: Major League Baseball

For this study we conducted exploratory data analysis to describe the increment of payroll in each year. Rather than taking the difference in payroll, we used the log difference in payroll. For example, rather than taking the difference of 2013 payroll - 2012 payroll, we took the log(2013 payroll) - log(2012 payroll). We used the log difference to prove the payroll gap percentage.

The table below shows total change in payroll from 2010 - 2014 inclusive. The column change in Overall_Change_Payroll, takes the incremental sum of change in payroll from 2010-2014. Based on this, the Los Angeles Dodgers, had the greatest change in payroll. Please refer to the table below for the other following teams.

Team	Sum of log change in payroll	Average_Payroll	Aggregate_Wins	Aggregate_Wins_Pct
Los Angeles Dodgers	0.8511002	149.15418	434	2.682156
Washington Nationals	0.8200017	91.04086	429	2.651215
San Diego Padres	0.7443947	59.23019	390	2.407407
Texas Rangers	0.6839576	103.63741	437	2.694085
San Francisco Giants	0.6294727	125.62321	436	2.691358

The graph below shows the change in log payroll difference from year to year.

The table below shows the difference in win percentage from 2010 to 2014 from greatest to least. The table shows that the Arizona diamondbacks had the greatest difference in log win percentage from 2014 to 2010.

Team	Difference of log win Percent	Aggregate_Wins
Arizona Diamondbacks	0.1790123	385
Boston Red Sox	0.1728395	416
Cleveland Indians	0.1481481	394
Baltimore Orioles	0.1481481	409
Los Angeles Angels	0.1234568	431

The teams with the largest total change in payroll have been highlighted in the chart below.

Yearly payroll or yearly increase in payroll

We would argue that increase in payroll on the log scale does not lead to better performance. Referring to the table which includes overall change in payroll, there are very little differences in aggregate win percentage despite having a wide range of overall payroll between the top 5 teams.

To compared if payroll or log increase in payroll was more effective, we regressed win percentage on payroll and log_Payroll_Diff and compared the r-squared values. Payroll gave an r-squared value of 0.1173386 and log payroll in crease gave an r-squared value of 0.0089299. Based on these two r-sqaured values we determined that payroll is more effective in explaining performance.

Homework1

Ying Dai, Jonathon Sun, Joyce Zhang

1/27/2021